Anti-regime guerillas have battled to stave off an onslaught by forces loyal to President Bashar al-Assad in Aleppo on Sunday as the government claimed it had defeated a rebel assault in Damascus.

Despite days of heavy skirmishes in the south-west of Syria's second city, a decisive battle is yet to begin. The rebels are in control of a crescent-shaped area, from the east to the south and centred on the suburb of Salahedine.

The Free Syrian Army (FSA) has set up a network of checkpoints in the neighbourhoods it controls, run by young militia fighters, many of them extremely nervy. It remains encamped in much of the hinterland to the north of the city, which it entered on 20 July, and troops are using anti-regime villages in these areas to move reinforcements into Aleppo.

Large numbers of residents have fled the city for Turkey since the rebel advance. Many of those who escaped to Damascus when the fighting peaked more than a week ago are yet to return, citizens in the worst-affected suburbs including Qabboun and Midan told the Guardian on Sunday night. "It's not back to normal, not even close," said one man. "This Ramadan is the worst ever. We are all to scared to celebrate."

On Monday morning the Reuters news agency reported the regime was claiming to have recaptured parts of Aleppo. "Complete control of Salahedine has been [won back] from those mercenary gunmen," an unidentified military officer reportedly told Syrian state television. "In a few days safety and security will return to the city of Aleppo."

Reuters said it was unable to confirm the report and the pro-opposition Syrian Observatory for Human rights said fighting was continuing in Salaheddine.

Syrian forces have been steadily gathering armour and troops on the outskirts of Aleppo, many parts of which are believed to remain loyal to the regime. The foreign minister, Walid Moualem, on Sunday claimed rebel fighters had been ousted from neighbourhoods in Damascus they had held for more than 10 days. Speaking during a visit to Iran, Mouallem said of the rebel campaign: "So they moved on to Aleppo. I assure you their plots will fail."

The coming battle is seen by both sides as a crucial phase in the uprising. Rebels advanced without the heavy weapons they had been pleading for, apparently trying to capitalise on momentum gained during the Damascus assault and the bombing of a government intelligence hub which killed four generals who had organised the regime's crackdown.

One military commander in Aleppo's rebel-held Boustan Alkasr province said shelling had continued all weekend. The commander, who declined to be named, was pessimistic about the FSA's chances of fending off repeated attacks. "The FSA has several hundred soldiers stationed inside Aleppo and in total a bigger force in the area of around 2,000," he said. "The regime has 100 tanks, we estimate, and about another 400 troop carriers and armoured vehicles. They also have 43 buses of Shabiha [militia] that have been brought inside Aleppo, with around 1,500 soldiers. And the regime has helicopters."

The commander said unless the opposition could get access to heavy weapons it would take "two to three years" to defeat Assad's military machine. He did not think Damascus would wage a large-scale frontal assault on Aleppo; instead it would bomb rebel-held districts from the sky. He added that the regime had flown fighter jets over the city, not to fire rockets but to frighten residents – tens of thousands of whom have already fled.

Rebel groups inside the city are struggling to communicate. They have walkie-talkies but the regime has hacked communications, with the internet and other services erratic.

Inside Aleppo, residents in FSA areas said they supported the Syrian revolt, but complained of shortages of bread and fuel and were terrified by the constant presence of helicopter gunships.

In Boustan Alkasr at least 100 people queued outside a bakery on Saturday. "We have nothing to eat," one woman said, according to video footage smuggled out by activists.